It sounds like your father got a loan and you are making the payments.
If your name and SSN are not on the loan then you are not getting credit for making the payments your father is. So it will not affect your credit. If you are on the loan as a secondary borrower it will affect your credit but not substantially on the positive but could affect it substantially on the negative side.
Since your father is named as the primary borrower you will probably need to talk with him about it first. If this is a mistake the 2 of you will need to work together with the bank to get it corrected. Since your father is currently listed first the bank is probably going to be unable(even if they are willing) to make a change to the loan now with out his explicit permission.
In addition if the loan is in your fathers name, if it is a vehicle loan, then the car is most likely in your fathers name as well. Most states require that the primary signatory on a vehicle loan also be the primary owner on the title to the vehicle. If your fathers name is the primary name on the title then you would have to retitle the car to refinance in your name.